2.3.185 Problems 18401 to 18500

Table 2.943: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
18401	24276	\begin{align*} \sin \left (\theta \right ) r^{\prime }&=-1-2 r \cos \left (\theta \right ) \\ \end{align*}	✓	✓	✓	✓	3.265
18402	19239	\begin{align*} \left (y \cos \left (y\right )-\sin \left (y\right )+x \right ) y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	3.266
18403	1735	\begin{align*} 3 x^{2} y^{2}+2 y+2 x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.267
18404	26901	\begin{align*} y^{\prime }+y x&=x y^{2} \\ \end{align*}	✓	✓	✓	✓	3.267
18405	2544	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	3.268
18406	8474	\begin{align*} e^{\prime }&=-\frac {e}{r c} \\ e \left (4\right ) &= e_{0} \\ \end{align*}	✓	✓	✓	✓	3.268
18407	18513	\begin{align*} \frac {y}{t}+y^{\prime }&=5+\cos \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	3.268
18408	22768	\begin{align*} \left (2 x +3\right )^{2} y^{\prime \prime }+\left (2 x +3\right ) y^{\prime }-2 y&=24 x^{2} \\ \end{align*}	✓	✓	✓	✗	3.268
18409	17638	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-16 y&=\ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.269
18410	18083	\begin{align*} {y^{\prime }}^{4}&=1 \\ \end{align*}	✓	✓	✓	✓	3.269
18411	21038	\begin{align*} x^{\prime }&=\ln \left (x^{2}+1\right ) \\ \end{align*}	✓	✓	✓	✓	3.269
18412	1206	\begin{align*} -1+9 x^{2}+y+\left (x -4 y\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	3.270
18413	13915	\begin{align*} \left (x^{n}+a \right )^{2} y^{\prime \prime }-b \,x^{-2+n} \left (\left (b -1\right ) x^{n}+a \left (n -1\right )\right ) y&=0 \\ \end{align*}	✗	✓	✗	✗	3.270
18414	8547	\begin{align*} x y^{\prime \prime }-5 y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	3.273
18415	12683	\begin{align*} \cos \left (x \right )^{2} y^{\prime \prime }-\left (\cos \left (x \right )^{2} a +\left (n -1\right ) n \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	3.273
18416	4272	\begin{align*} y^{\prime }+y \cot \left (x \right )&=2 x \csc \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.274
18417	6314	\begin{align*} y y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.274
18418	8641	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 4 t & 0<t <1 \\ 8 & 1<t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	3.275
18419	25023	\begin{align*} y^{\prime }&=\sin \left (t -y\right ) \\ \end{align*}	✓	✓	✓	✓	3.275
18420	27541	\begin{align*} {y^{\prime \prime }}^{2}&=1+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	3.275
18421	4759	\begin{align*} x y^{\prime }&=\sin \left (x \right )-2 y \\ \end{align*}	✓	✓	✓	✓	3.276
18422	24268	\begin{align*} y^{\prime }&={\mathrm e}^{x +y} \\ \end{align*}	✓	✓	✓	✓	3.276
18423	8620	\begin{align*} y^{\prime \prime }+\frac {y}{4 x}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.277
18424	17859	\begin{align*} y^{\prime }&=y-x^{2} \\ \end{align*}	✓	✓	✓	✓	3.277
18425	4643	\begin{align*} y^{\prime }&=\sin \left (2 x \right )-y \tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.278
18426	26662	\begin{align*} x y^{\prime \prime }-y^{\prime }-4 x^{3} y&=16 x^{3} {\mathrm e}^{x^{2}} \\ \end{align*}	✓	✓	✓	✗	3.278
18427	20268	\begin{align*} y-x \sin \left (x^{2}\right )+x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.279
18428	19796	\begin{align*} x \left (-x^{2}+1\right ) y^{\prime }+\left (2 x^{2}-1\right ) y&=a \,x^{3} \\ \end{align*}	✓	✓	✓	✓	3.280
18429	11382	\begin{align*} y^{\prime }+2 \tan \left (y\right ) \tan \left (x \right )-1&=0 \\ \end{align*}	✗	✓	✓	✗	3.281
18430	15510	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	3.281
18431	5036	\begin{align*} y y^{\prime }+x \,{\mathrm e}^{x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	3.283
18432	19231	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.283
18433	20796	\begin{align*} x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+a^{2} y&=\frac {1}{x^{2}} \\ \end{align*}	✓	✓	✓	✗	3.283
18434	26659	\begin{align*} y^{\prime \prime }+y^{\prime }+y \,{\mathrm e}^{-2 x}&={\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✗	3.283
18435	15851	\begin{align*} y^{\prime }&=y \left (-1+y\right ) \left (y-3\right ) \\ y \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✗	✗	3.286
18436	23857	\begin{align*} \left (x^{3}+1\right ) y^{\prime }+x y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	3.287
18437	10256	\begin{align*} x^{2} y^{\prime }+{\mathrm e}^{-y}&=0 \\ \end{align*}	✓	✓	✓	✓	3.288
18438	24375	\begin{align*} 3 x^{2}+3 y^{2}+x \left (x^{2}+3 y^{2}+6 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.288
18439	11527	\begin{align*} a y y^{\prime }+b y^{2}+f \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.289
18440	22765	\begin{align*} x^{2} y^{\prime \prime }+3 x y^{\prime }-3 y&=x^{2}-4 x +2 \\ \end{align*}	✓	✓	✓	✓	3.289
18441	23941	\begin{align*} y^{\prime }&=x^{2} y \\ \end{align*}	✓	✓	✓	✓	3.289
18442	55	\begin{align*} y^{\prime }&=\frac {\left (x -1\right ) y^{5}}{x^{2} \left (2 y^{3}-y\right )} \\ \end{align*}	✓	✓	✓	✗	3.290
18443	719	\begin{align*} y^{\prime }&=\left (1-y\right ) \cos \left (x \right ) \\ y \left (\pi \right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	3.290
18444	19116	\begin{align*} y^{2} \left (y^{\prime }-1\right )&=\left (2-y^{\prime }\right )^{2} \\ \end{align*}	✓	✓	✓	✓	3.290
18445	8604	\begin{align*} x y^{\prime \prime }+5 y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.291
18446	17210	\begin{align*} 2 t +y^{3}+\left (3 t y^{2}+4\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.291
18447	1133	\begin{align*} y^{\prime }&=\cos \left (x \right )^{2} \cos \left (2 y\right )^{2} \\ \end{align*}	✓	✓	✓	✗	3.292
18448	7816	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}}&=\ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.292
18449	17077	\begin{align*} 3 \sin \left (x \right )-4 \cos \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.292
18450	19803	\begin{align*} \left (1+{\mathrm e}^{y}\right ) \cos \left (x \right )+{\mathrm e}^{y} \sin \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.292
18451	24246	\begin{align*} y-x +x y \cot \left (x \right )+x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.292
18452	205	\begin{align*} 3 y+x^{3} y^{4}+3 x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.293
18453	11474	\begin{align*} x \left (x^{2}-1\right ) y^{\prime }-\left (2 x^{2}-1\right ) y+a \,x^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	3.294
18454	4215	\begin{align*} y^{\prime }&={\mathrm e}^{x -y} \\ \end{align*}	✓	✓	✓	✓	3.295
18455	4057	\begin{align*} 4 x^{2} y^{\prime \prime }-\left (4 x +3\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.296
18456	17814	\begin{align*} x^{\prime \prime }+x&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 2-t & 1\le t <2 \\ 0 & 2\le t \end {array}\right . \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.296
18457	12938	\begin{align*} y y^{\prime \prime }+a {y^{\prime }}^{2}+y^{3} b&=0 \\ \end{align*}	✓	✓	✓	✗	3.297
18458	18338	\begin{align*} \left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y&=\left (x -1\right )^{2} {\mathrm e}^{x} \\ y \left (-\infty \right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✗	✗	3.297
18459	3455	\begin{align*} y^{\prime }&=-\cot \left (t \right ) y+6 \cos \left (t \right )^{2} \\ y \left (\frac {\pi }{4}\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	3.298
18460	2338	\begin{align*} 1+{\mathrm e}^{y t} \left (1+y t \right )+\left (1+{\mathrm e}^{y t} t^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.299
18461	4754	\begin{align*} x y^{\prime }&=1+x^{3}+y \\ \end{align*}	✓	✓	✓	✓	3.300
18462	6493	\begin{align*} a y y^{\prime \prime }&=\left (a -1\right ) {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	3.300
18463	23892	\begin{align*} x^{4}-3 y+3 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.300
18464	14961	\begin{align*} x^{\prime \prime }-4 x^{\prime }&=\tan \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	3.301
18465	15550	\begin{align*} y^{\prime }&=\sqrt {\left (y+2\right ) \left (-1+y\right )} \\ \end{align*}	✓	✓	✓	✓	3.301
18466	27219	\begin{align*} 2 x^{2} y y^{\prime }+y^{2}&=2 \\ \end{align*}	✓	✓	✓	✓	3.301
18467	4198	\begin{align*} x y^{\prime }-n y&=x^{n} \\ \end{align*}	✓	✓	✓	✓	3.302
18468	4646	\begin{align*} y^{\prime }&=\csc \left (x \right )+3 y \tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.303
18469	6406	\begin{align*} -6+x y \left (12+3 y x -2 x^{2} y^{2}\right )+x^{2} \left (9+2 y x \right ) y^{\prime }+2 x^{3} y^{\prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	3.303
18470	7160	\begin{align*} y^{\prime }+b^{2} y^{2}&=a^{2} \\ \end{align*}	✓	✓	✓	✓	3.303
18471	7527	\begin{align*} \left (x^{2}-\frac {2}{y^{3}}\right ) y^{\prime }+2 y x -3 x^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	3.303
18472	20305	\begin{align*} y^{\prime }&=\frac {1+x^{2}+y^{2}}{2 x y} \\ \end{align*}	✓	✓	✓	✓	3.303
18473	24192	\begin{align*} w^{3}+w z^{2}-z+\left (z^{3}+w^{2} z-w \right ) z^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.303
18474	25673	\begin{align*} y x +x^{2} y^{\prime }&=10 \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.305
18475	4295	\begin{align*} x +y+\left (x -y\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.306
18476	8436	\begin{align*} \cos \left (x \right ) y^{\prime }+y \sin \left (x \right )&=1 \\ \end{align*}	✓	✓	✓	✓	3.306
18477	9888	\begin{align*} x^{2} y^{\prime \prime }+5 x y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.306
18478	12036	\begin{align*} y^{\prime }&=\frac {y x +x^{3}+x y^{2}+y^{3}}{x^{2}} \\ \end{align*}	✓	✓	✓	✗	3.306
18479	23899	\begin{align*} 3 x^{2} y \ln \left (y\right )+\left (2 x^{3}+2 y^{3}+3 y^{3} \ln \left (y\right )^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.306
18480	22656	\begin{align*} 4 y^{\prime \prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.308
18481	5356	\begin{align*} {y^{\prime }}^{2}&=x -y \\ \end{align*}	✓	✓	✓	✓	3.310
18482	11481	\begin{align*} x \left (x^{3}-1\right ) y^{\prime }-2 x y^{2}+y+x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	3.310
18483	12959	\begin{align*} 2 y y^{\prime \prime }-3 {y^{\prime }}^{2}-4 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	3.310
18484	182	\begin{align*} 2 x y^{3}+{\mathrm e}^{x}+\left (3 x^{2} y^{2}+\sin \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.314
18485	15462	\begin{align*} y^{\prime }+\frac {y}{x}&={\mathrm e}^{x} \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.314
18486	8526	\begin{align*} y^{\prime \prime }+\frac {3 y^{\prime }}{x}-2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.315
18487	2476	\begin{align*} t^{2} y+y^{\prime }&=t^{2} \\ \end{align*}	✓	✓	✓	✓	3.316
18488	17981	\begin{align*} x^{2}+y-x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.316
18489	19086	\begin{align*} x -y^{2}+2 x y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.317
18490	26202	\begin{align*} y^{\prime }&=\frac {x -1}{y} \\ \end{align*}	✓	✓	✓	✓	3.318
18491	3671	\begin{align*} y^{\prime }&=\left (9 x -y\right )^{2} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.319
18492	4361	\begin{align*} 1-\left (1+2 x \tan \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.319
18493	4716	\begin{align*} y^{\prime }&=a +b \cos \left (A x +B y\right ) \\ \end{align*}	✓	✓	✓	✗	3.319
18494	10405	\begin{align*} y {y^{\prime \prime }}^{2}+{y^{\prime }}^{3}&=0 \\ \end{align*}	✓	✓	✓	✗	3.319
18495	12425	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-y-a \,x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	3.319
18496	18514	\begin{align*} -2 y+y^{\prime }&=3 \,{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	3.319
18497	4662	\begin{align*} y^{\prime }&=\cos \left (2 x \right )+\left (\sin \left (2 x \right )+y\right ) y \\ \end{align*}	✓	✓	✓	✗	3.320
18498	13951	\begin{align*} y^{\prime \prime }+\left (a \,{\mathrm e}^{\lambda x}+b \right ) y^{\prime }+\left (\alpha \,{\mathrm e}^{2 \lambda x}+\beta \,{\mathrm e}^{\lambda x}+\gamma \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	3.320
18499	17188	\begin{align*} y+y^{\prime }&=4+3 \,{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	3.320
18500	24793	\begin{align*} 4 x -2 y y^{\prime }+{y^{\prime }}^{2} x&=0 \\ \end{align*}	✓	✓	✓	✓	3.320